#### Question

The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

#### Solution

Let the speed of stream be x km/hr then

Speed downstream = (8 + x)km/hr.

Therefore, Speed upstream = (8 - x)km/hr

Time taken by the boat to go 15km upstream `15/(8-x)hr`

Time taken by the boat to returns 22km downstream `22/(8+x)hr`

Now it is given that the boat returns to the same point in 5 hr.

So,

`15/(8-x)+22/(8+x)=5`

`(15(8+x)+22(8-x))/((8-x)(8+x))=5`

`(120+15x+176-22x)/(64-x^2)=5`

`(296-7x)/(64-x^2)=5`

5x^{2} - 7x + 296 - 320 = 0

5x^{2} - 7x - 24 = 0

5x^{2} - 15x + 8x - 24 = 0

5x(x-3) + 8(x - 3) = 0

(x - 3)(5x + 8) = 0

x - 3 = 0

x = 3

Or

5x + 8 = 0

5x = -8

x = -8/5

But, the speed of the stream can never be negative.

Hence, the speed of the stream is x = 3 km/hr